Related papers: Coupled Input-Output Dimension Reduction: Applicat…
We consider the problem of reducing the dimensions of parameters and data in non-Gaussian Bayesian inference problems. Our goal is to identify an "informed" subspace of the parameters and an "informative" subspace of the data so that a…
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior…
In applications involving ordinal predictors, common approaches to reduce dimensionality are either extensions of unsupervised techniques such as principal component analysis, or variable selection procedures that rely on modeling the…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Scaling Bayesian optimization to high dimensions is challenging task as the global optimization of high-dimensional acquisition function can be expensive and often infeasible. Existing methods depend either on limited active variables or…
In this thesis, I explore the possibilities of conducting Bayesian optimization techniques in high dimensional domains. Although high dimensional domains can be defined to be between hundreds and thousands of dimensions, we will primarily…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Bayesian optimization works effectively optimizing parameters in black-box problems. However, this method did not work for high-dimensional parameters in limited trials. Parameters can be efficiently explored by nonlinearly embedding them…
Bayesian optimization (BO ) is an effective method for optimizing expensive-to-evaluate black-box functions. While high-dimensional problems can be particularly challenging, due to the multitude of parameter choices and the potentially high…
The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of…
A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…
Bayesian optimization (BO) has shown impressive results in a variety of applications within low-to-moderate dimensional Euclidean spaces. However, extending BO to high-dimensional settings remains a significant challenge. We address this…
Bayesian optimal experimental design (BOED) selects experiments to maximize information gain about model parameters. However, in decision-critical settings, reducing parameter uncertainty does not necessarily improve downstream decisions,…
Bayesian optimization (BO) is a powerful approach for seeking the global optimum of expensive black-box functions and has proven successful for fine tuning hyper-parameters of machine learning models. However, BO is practically limited to…
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
Bayesian Optimization (BO) has shown significant success in tackling expensive low-dimensional black-box optimization problems. Many optimization problems of interest are high-dimensional, and scaling BO to such settings remains an…
This paper presents a novel framework for goal-oriented optimal static sensor placement and dynamic sensor steering in PDE-constrained inverse problems, utilizing a Bayesian approach accelerated by low-rank approximations. The framework is…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…